In　this　paper,　we　consider　the　streaming　sequence　submodular　maximization　problem,　in　which　the　utility　function　is　defined　on　sequences　of　element　instead　of　element　sets.　We　encode　the　values　of　different　sequences　by　a　weighted　directed　acyclic　graph　(W-DAG),　where　the　weight　of　vertex　reveals　the　utility　value　in　selecting　single　element　and　the　weight　of　an　edge　proclaims　the　additional　benefit　according　to　a　certain　selected　order.　In　addition,　the　edges　are　revealed　in　a　streaming　fashion　that　one　edge　is　known　in　one　time　slot.　The　aim　is　to　output　a　sequence　of　vertices　of　length　bounded　by　a　given　constant　k,　such　that　the　utility　function　value　is　maximized.　In　this　work,　we　first　provide　the　framework　of　the　sequence　submodular　maximization　under　streaming.　By　utilizing　an　edge-based　thresholding　principle,　we　derive　a　one　pass,　-approximation　algorithm　with　memory　and　update　time　per　edge,　where　and　is　the　maximum　in-degree　(out-degree)　of　the　constructed　W-DAG.　At　last,　we　present　a　further　improved　streaming　algorithm,　which　also　requires　one　pass　over　the　stream　and　attains　the　same　approximation　ratio　but　is　with　a　decreased　memory　complexity　of.　©　2019,　Springer　Nature　Switzerland　AG.